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Given the collinear points A,B,C find the coordinates of C(2t,1-t) if A(3,3), B(2,4).

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Given the collinear points A,B,C find the coordinates of C(2t,1-t) if A(3,3), B(2,4).

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We'll use determinants to compute the coordinates of C.

We'll create the determinant of the coordinates of the given collinear points. The value of this determinant is zero if the points are collinear.

|3    3    1|

D =  |2    4    1|

|2t  (1-t) 1|

We'll calculate D:

D = 3*4*1 + 2(1-t)*1 + 2t*3*1 - 2t*4*1 - 3(1-t) -  2*3*1

D = 12 + 2 - 2t + 6t - 8t - 3 + 3t - 6

D = 5 - t

Since A,B,C are collinear => D = 0 <=> 5 - t = 0

t = 5

The coordinates of C are: C(10 , -4).

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